Consider the relation R(P, Q, S, T, X, Y, Z, W) with the following functional dependencies.

PQ → X; P → YX; Q → Y; Y → ZW

Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.

D1 : R = [(P, Q, S, T); (P, T, X); (Q, Y); (Y, Z, W)]

D2 : R = [(P, Q, S); (T, X); (Q, Y); (Y, Z, W)]

Which one of the following options is correct?

1

D1 is a lossy decomposition, but D2 is a lossless decomposition.

2
Both D1 and D2 are lossless decompositions.
3
Both D1 and D2 are lossy decompositions.
4
D1 is a lossless decomposition, but D2 is a lossy decomposition.

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